en 1998-3: eurocode 8: design of structures for earthquake … · en 1998-3 (2005) (english):...

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EN 1998-3 (2005) (English): Eurocode 8: Design of structuresfor earthquake resistance – Part 3: Assessment andretrofitting of buildings [Authority: The European Union PerRegulation 305/2011, Directive 98/34/EC, Directive2004/18/EC]

EUROPEAN STANDARD EN 1998-3

NORME EUROPEENNE

EUROpAISCHE NORM June 2005

ICS 91.120.25 Supersedes ENV 1998-1-4:1996

Incorporating corrigendum March 2010

English version

Eurocode 8: Design of structures for earthquake resistance -Part 3: Assessment and retrofitting of buildings

Eurocode 8: Calcul des structures pour leur resistance aux seismes - Partie 3: Evaluation et renforcement des

batiments

Eurocode 8: Auslegung von Bauwerken gegen Erdbeben Teil 3: Beurteilung und ErtUchtigung von Gebauden

This European Standard was approved by CEN on 15 March 2005.

CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such national standards may be obtained on application to the Central Secretariat or to any CEN member.

This European Standard exists in three official versions (English, French, German). A version in other language made by translation under the responsibility of a CEN member into its own language and notified to the Central .

BS EN 1998-3:2005 EN 1998-3:2005 (E)

Contents Page

FORE\VORD .................................................................................................................. 4

1 G ENE I~A L .............................................................................................................. 9

1.1 SCOPE ................................................................................................................... 9 1.2 NORIV1ATIVE REFERENCES ............................................................................... 10

1.2.1 General reference standard., .................................................................. 10 1.3 ASSLIMPTIONS .................................................................................................... . 10 1.4 DISTINCTION BET\VEEN PRINCIPLES AND APPLICATION RULES .................. 10 1.5 DEFIN1TIONS ...................................................................................................... 10 1.6 SYIVIBOLS ........................................................................................................... 10

1.6.1 GeJ1eral ................................................................................................... 10 1.6.2 Symbols u5,'ed in Annex A ........................................................................ 10 1.6.3 SymboL,,;' used in Annex B ........................................................................ 12

1.7 S .1. U N 11~S ••..•..•••..•••••••••..•••.••.•••••••••••..•..•.••••••••••••••.••••••••••••••••••••••••••••••••••.••••••••• 13

2 PERFORlVlANCE REQUIREME~TS AND COMPLIA~CE CRITERIA ... 14

2.1 FUNDAM.ENTAL REQUIREI\1EN crS ..................................................................... 14 2.2 COMPLJANC.E CRJTEllll\ ................................................................................... 15

2.2.1 General .......................... ......................................................................... 15 2.2.2 Limit State ofl/ear Collapse (1\fC) ......................................................... 15 2.2.3 Limit State of Signtficant Damage (SD) ................................................. 16

4 Limit State of Dam age Li/nitation (DL) ...................... ............................ 16

3 IN FORJ\lATION FOR STRUCTURAL ASSESSMENT ................................. 17

3.1 GENERAL .INFORMATION AND HISTORY ......................................................... 17 3.2 REQUIRED INPUT DA1'A .................................................................................... 17 3.3 KNO\VlJEDGE LEVELS ....................................................................................... 18

3.3.1 Definition of kn01Nledge levels .... ............................................................ 18 3.3.2 1([1: Limited knowledge ......................................................................... 19 3.3.3 KL2: JVormal knowledge .............................................. ........................... 20 3.3.4 KL3: Full knowledge .............................................................................. 20

3.4 IDENTIFICATION OF THE KNOWLEDGE LEVEL ............................................. 21 3.4.1 Geol11etlY ................................................................................................ 21 3.4.2 Det(Jils ........................................................................ ............................. 22 3.4.3 Materials ............................................................... ................................. . 3.4.4 Definition o.fthe levels of inspection and testing ................................... 23

3.5 CONFIDENCE FACTORS .................................................................................... 23

4 ASSESSNIENT ...................................................................................................... 24

4.1 GEN EJ{AL ........................................................................................................... 24 4.2 SEISM IC ACTION AND SEISlVIlC LOAD COJ\1BINATION .................................... 24 4.3 STRlJCcrURAL MODELLING ............................................................................... 24 4.4 METHODS OF i\NAL \:TSIS ................................................................................... 25

4.4.1 Gel1el·al ............................................. ...................................................... 25 4.4.2 Lateralforce analysis ............................................................................. 25 4.4.3 kfulti-modal response spectrum analysis ............................................... 26 4.4.4 Nonlinear static ana~ysis ........................................................................ 26 4.4.5 iVon-linear time-histor,v analysis ............................................................ 27 4.4.6 q-.fi7ctor c7pproclch ................................................................................... 27

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4.4.7 Combination of the components of the seismic action ........................... 27 4.4.8 Additional measuresfor masonry in filled structures ............................. 28 4.4.9 Combination coefficients for variable actions ....................................... 28 4.4.10 importance classes and importance factors ........................................... 28

4.5 SAFETY V'ERIFICA'fIONS ................................................................................... 28 4.5.1 Linear methods of analysis (lateral force or modal response spectrum analysi5) 28 4.5.2 Nonlinear method,> of analysis ~s'tatic or dynamic) ................................ 29 4.5.3 q:factor approach ................................................................................... 29

4.6 SU.MlVIARY OF CRITERIA FOR ANALYSIS AND SAFETY VERIFICATIONS ....... 29

5 DECISIONS F'OR STRUCTURAL INTERVENTION .................................... 31

5.1 CRITERIA FOR A STRUCTURAL INTERVENTION ............................................. 31 5.1.1 Introduction ............................................................................................ 31 5.1.2 Technical criteria ................................................................................... 31 5.1.3 Type of intervention ................................................................................ 31 5.1.4 Non-structural elements ......................................................................... 32 5.1.5 lust[fication of the selected intervention type ...... .................................. 32

6 DESIGN OF STRUCTURAL INTERVENTION .............................................. 34

6.1 RETROFIT DESIGN PROCEDURE ....................................................................... 34

ANNEX A (INFORMATIVE) REINFORCED CONCRETE STRUCTURES.35

ANNEX B (INFORMATIVE) STEEL AND COMPOSITE STRUCTURES ... 55

ANNEX C (INFORMATIVE) MASONRY BUILDINGS ................................... 81

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Foreword

This European Standard EN 1998-3, Eurocode 8: Design of structures for earthquake Assessnlent and Retrofitting of buildings, has been prepared by Technical

Comnlittee CEN/TC 250 "Structural Eurocodes", the secretariat of vvhich is held by BSL CEN/TC 250 is responsible for all Structural Eurocodes.

This European Standard shall be given the status of a national standard, either by publication of an identical text or by endorsement, at the latest by December 2005, and conflicting national standards shall be withdrawn at the latest by March 2010.

This dOCUl11ent supersedes ENV 1998-1 1996.

According to CEN-CENELEC Internal Regulations, the National Standard Organisations of the following countries are bound to inlplement this European Standard: Austria, Belgium, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Gernlany, Greece, Hungary, Iceland, Ireland, Italy, Lithuania, Luxenlbourg, Malta, Netherlands, Norway, Poland, Portugal, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdoll1.

Background of the Eurocode programme

In 1975, the Comnlission of the European Con1111unity decided on an action progranl1ue in the field of construction, based on article 95 of the Treaty. The objective of the progranl1ne was the elinlination of technical obstacles to trade and the harn10nisatioll of technical specifications.

Within this action progranlme, the COlnnlission took the initiative to establish a set of hannonised technical rules for the design of construction works which, in a first stage, would serve as an alternative to the national rules in force in the Member States and, ultilnately, would replace then1.

For fifteen years, the Conlll1ission, with the help of a Steering Conlnlittee with Representatives of Menlber States, conducted the develop111ent of the Eurocodes progranl1ne, which led to the first generation of European codes in the 1980' s.

In 1989, the Conlnlission and the MelTlber States of the EU and EFTA decided, on the basis of an agreel11ent l between the C01111nission and CEN, to transfer the preparation and the publication of the Eurocodes to CEN through a series of Mandates, in order to provide them with a future status of European Standard (EN). This links de facto the Eurocodes with the provisions of all the Council's Directives and/or Con1mission's Decisions dealing vvith European standards the Council Directive 89/106/EEC on construction products - CPD - and Council Directives 93/37/EEC, 92/50/EEC and 89/440lEEC on pub1ic works and and equivalent EFTA Directives initiated in pursuit of setting up the internal market).

The Structural Eurocode progranlnle con1pnses the following standards generally consisting of a nU111ber of Parts:

I Agreement between the Commission of the European Communities and the European Committee for Standardisation (CEN) concerning the work on EUROCODES for (he design of building and eivil engineering works (BCiCEN/03/89),

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EN 1990 Eurocode:

EN 1991 Eurocode 1:

EN 1992 Eurocode 2:

EN 1993 Eurocode 3:

Basis of structural design

Ac60ns on structures

Design of concrete structures

Design of steel structures

BS EN 1998-3:2005 EN 1998-3 :2005 (E)

EN 1994 Eurocode 4: Design of cOlnposite and concrete structures

EN 1995 Eurocode 5: Design of tinlber structures

EN 1996 Eurocode 6: Design of Inasonry structures

EN 1997 Eurocode 7: Geotechnical design

EN 1998 Eurocode 8: Design of structures for earthquake resistance

EN 1999 Eurocode 9: Design of aluminiulTI structures

Eurocode standards recognise the responsibility of regulatory authorities in each Menlber State and have safeguarded their right to determine values related to regulatory safety lTIatters at national level where these continue to vary fronl State to State.

Status and field of app1ication of Eurocodes

The Menlber States of the and EFTA recognise that Eurocodes serve as reference doclllnents for the following purposes:

as a ll1eans to prove conlpliance of building and civil engineering works with the essential requirements of Councjl Directive 89/106/EEC, particularly Essential Requirenlent N° 1 Mechanical resistance and stability - and Essential Requirenlent N°2 - Safety in case of fire;

as a basis for specifying contracts for construction works and related engineering services;

as a framework for drawing up hannonised technical specifications for construction products (ENs and ETAs)

The Eurocodes, as far as they concenl the construction works thelllselves, have a direct relationship with the Interpretative Documents2 referred to in Article 12 of the CPD, although they are of a different nature tl'0111 hannonised product standards3. Therefore, technical aspects arising fron1 the Eurocodes work need to be adequately considered by

According to Art. 3.3 of the CPO, the essential requirements (ERs) shall be given concrete form in interpretative documents for the creation of the necessary links between the essential requirements and the mandates for hENs and ET AGsiET As .

.1 According to Art. 12 onlle CPO the interpretative documents shall:

a) give concrete form to the essential requirements by harmonising the terminology and the technical bases and indicating classes or levels for each requirement where necessary;

b) indicate methods of corrdating these classes or levels of requirement with the technical specitications, e.g. methods of calculation and of proof, technical rulcs for project design, etc. ;

c) serve as a reference for the establishment of harmonised standards and guidelines tor European technical approvals.

The Euroeodes, de/clcfo, playa similar role in the field of the ER 1 and a part of ER 2.

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CEN Technical Committees and/or EOTA Working Groups working on product standards with a view to achieving a full conlpatibility of these technical specifications with the Eurocodes.

The Eurocode standards provide comnl0n structural design rules for everyday use for the design of whole structures and conlponent products of both a traditional and an innovative nature. Unusual fonns of construction or design conditions are not specifically covered and additional expert consideration win be required by the designer in such cases.

National Standards implenlenting Eurocodes

The National Standards ill1plenlenting Eurocodes will comprise the full text of the Eurocode (including any annexes), as published by CEN, which may be preceded by a National title page and National foreword, and Inay be followed by a National annex (inforn1ative ).

The National annex nlay only contain infonnation on those parameters which are left open in the Eurocode for national choice, known as Nationally Determined Parmneters, to be used for the design of buildings and civil engineering works to be constructed in the country concerned,

values and/or classes where alternatives are given in the Eurocode,

values to be used \vhere a synlbol only is given in the Eurocode,

country specific data (geographical, clinlatic, etc.), e.g. snow n1ap,

the procedure to be used where alternative procedures are given in the Eurocode.

It Jnay also contain

decisions on the application of infonnative annexes,

references to non-contradictory c01nplenlentary information to assist the user to apply the Eurocode.

Links between Eurocodes and harmonised technical specifications (ENs and ETAs) for products

There is a need for consistency between the harn10nised technical specifications for construction products and the technical rules for works4. Furthernl0re, all the info1111atio11 acco111panying the CE Marking of the construction products which refer to Eurocodes shall clearly n1entl0n which Nationally Determined Parameters have been taken into account.

Additional information specific to EN 1998-3

Although asseSSlnellt and retrofitting of existing structures for non-seislnic actions is not yet covered by the relevant ll1aterial-dependent Eurocodes, this Part of Eurocode 8 was specifically developed because:

-1 See ArL3.3 and Arl.l of the CPO, well LIS clauses 4.2, 4.3.1,4.3.2 and 5.2 of 10 I.

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- For many older structures~ seislnic resistance was not considered during the original construction, whereas non-SeiS111ic actions were catered for, at least by means of traditional construction rules.

- Seisnlic hazard evaluations in accordance with present knowledge may indicate the need for retrofitting canlpaigns.

Danlage caused by earthquakes nlay create the need for nlajor repairs.

Furthennore, since within the philosophy of Eurocode 8 the SeiS111ic design of new structures is based on a certain acceptable of structural damage in the event of the design earthquake, criteria for seismic asseSSlllent (of structures designed in accordance with Eurocode 8 and subsequently danlaged) constitute an integral part of the entire process for seisl11ic structural safety.

In seismic retrofitting situations, qualitative verifications for the identification and elinlination of 111ajor structural are very inlportant and should not be discouraged by the quantitative analytical approach proper to this Part of Eurocode 8. Preparation of documents of more qualitative nature is left to the initiative of the National Authorities.

This Standard addresses only the structural aspects of seisnlic assessnlent and retrofitting, which nlay fOrl11 only one cOlllponent of a broader strategy for seismic risk 111itigation. This Standard will apply once the requirel11el1t to assess a particular building has been established. The conditions under which seisnlic assessnlent of individual buildings possibly leading to retrofitting ll1ay be required are beyond the scope of this Standard.

National progratllnles for seisnlic risk nlitigation through seismic assessnlent and retrofitting nlay differentiate between "active" and "passive" selsnlic aSSeSSl11ent and retrofitting progranl111es. "Active" progranlnles nlay require owners of certain categories of buildings to nleet specific deadlines for the conlpletion of the seismic asseSSlllent and depending on its outconle - of the retrofitting. The categories of buildings selected to be targeted nlay depend on seislnicity and ground conditions~ importance class and occupancy and perceived vulnerability of the building (as influenced by type of nlaterial and construction, nunlber of storeys, of the building with respect to dates of older code enforcenlent, etc.). "Passive" progranlnles associate seislnic asseSS111ent - possibly leading to retrofitting with other events or activities related to the use of the building and its continuity, such as a change in use that increases occupancy or inlportance class, rel110delling above certain limits (as a percentage of the building area or of the total building value), repair of damage after an earthquake, etc. The choice of the Limit States to be checked, as well as the return periods of the seisnlic action ascribed to the various Litnit States, nlay depend on the adopted progranlnle for assessnlent and retrofitting. The relevant requirements may be

stringent in "active" progran1111es than in "passive" ones; for example, in "passive" prograInllleS triggered by renlodelling, the relevant requiretnents 111ay gradate with the extent and cost of the remodelling work undertaken.

In cases of low seis111icity (see EN1998-J, 3.2.1(4)), this Standard ll1ay be adapted to local conditions by appropriate N ationa1 Annexes.

National annex for EN 1998-3

This standard gives altenlative procedures, values and recoll1nlendations for classes

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with notes indicating where national choices nlay have to be nlade. Therefore the National Standard inlplelnenting EN 1998-3: 2005 should have a National annex containing all Nationally Detell11ined Paranleters to be used for the design of buildings and civil engineering works to be constructed in the relevant country.

N' I I . atlona c 101ce IS a 11 owe d' EN 1998 3 2005 I 1 1 III - t lrougn causes: I

Reference ltelll I

1.1 (4) lnfornlative Annexes A, Band C.

2.1(2)P Nunlber of Limit States to be considered !

2.1(3)P Return period of seismic actions under which the Limit States should not

be exceeded.

2.2.1 (7)P Partial factors for nlaterials

3.3.1(4) Confidence factors

3.4.4(1) Levels of inspection and testing

4.4.2(1 )P MaxinlU1l1 value of the ratio Pmaxl Pmin

4.4.4.5(2) Complenlentary, non-contradictory information on non-linear static

analysis procedures that can capture the effects of higher modes.

I A.4.4.2(5) Partial factor 1ft! for FRP debonding

A.4.4.2(9) Partial factor j1(\ of the FRP

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1 GENERAL

1.1 Scope

BS EN 1998-3:2005 EN 1998-3:2005 (E)

(1) The scope of Eurocode 8 is defined in EN 1998-1: 2004, 1.1.1 and the scope of this Standard is defined in (2), (4) and (5). Additional parts of Eurocode 8 are indicated 111 1998-1: 2004, 1.1.3.

(2) The scope of EN 1998-3 is as follows:

To provide criteria for the evaluation of the selsn11C perfonnance of existing individual building structures.

- To describe the approach in selecting necessary corrective n1easures

To set forth criteria for the design of retrofitting ll1easures (i.e. conception, structural analysis including intervention 111easures, final dinlensioning of structural parts and their connections to existing structural elenlents).

NOTE For the purposes of this standard, retrofitting covers both the strengthening of undamaged structures and the repair of earthquake damaged structures.

(3) When designing a structural intervention to provide adequate resistance against seismic actions, structural verifications should also be tnade with respect to non-seisnlic load c0111binations.

(4) Reflecting the basic require111ents of EN 1998-1: 2004, this Standard covers the seisnlic asseSSlnent and retrofitting of buildings nlade of the more conll110nly used structural ll)aterials: concrete, steel, and masonry.

NOTE Informative Annexes Band C contain additional information related to the assessment of reinforced concrete, steel and composite, and masonry buildings, respectively, and to their upgrading when necessary.

(5) Although the provisions of this Standard are applicable to all categories of buildings, the seis111ic assessnlent and retrofitting of 1110nU111ents and historical buildings often requires different types of provisions and approaches, depending on the nature of the lnonUlnents.

(6) Since existing structures:

(i) ref1ect the state of knowledge at the tinle of their construction,

(ii) possibly contain hidden gross errors,

(iii) may have been sublnitted to previous earthquakes or other accidental actions with unknown effects,

structural evaluation and possible structural intervention are typically subjected to a different degree of uncertainty (level of knowledge) than the design of new structures. Different sets of material and structural safety factors are therefore required, as well as different analysis procedures, depending on the conlpleteness and reliability of the infonnation available.

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1.2 Normative references

(1)P This European Standard incorporates by dated or undated reference, provisions froll1 other publications. These normative references are cited at the appropriate places in the text and the publications are listed hereafter. For dated references, subsequent an1endn1ents to or revisions of any of these publications apply to this European Standard only when incorporated in it by mnendlnent or revision. For undated references the latest edition of the publication referred to applies (including an1endnlents ).

1.2.1 General reference standards

EN 1990 Eurocode - Basis of structural design

EN 1998-1 Eurocode 8 - Design of stIuctures for earthquake resistance - Part 1: General rules, seisn1ic actions and rules for buildings

1.3 Assumptions

(1) Reference is Inade to 1998-1: 2004, 1.3.

(2) The provisions of this Standard aSSUlne that the data collection and tests is perfornled by experienced personnel and that the engineer responsible for the assessn1ent, the possible design of the retrofitting and the execution of work has appropriate experience of the type of structures being strengthened or repaired.

(3) Inspection procedures, check-lists and other data-collection procedures should be docUlnented and filed, and should be referred to in the design documents.

1.4 Distinction between principles and application rules

(1) The rules of EN 1990: 2002, 1.4 apply.

1.5 Definitions

(1) Reference is made to EN 1998-1: 2004, 1.5.

1.6 Symbols

1.6.1 General

(1) Reference is made to 1998-1: 2004, 1.6.

(2) Further symbols used in this Standard are defined in the text where they occur.

1.6.2 Symbols used in Annex A

b width of steel straps in steel jacket

bo and ho din1ension of confined concrete core to the centreline of the hoop

bi centreline spacing of longitudinal bars

c concrete cover to reinforcen1ent

d effective depth of section (depth to the tension reinforcement)

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d' depth to the cOlnpression reinforcenlent

dbL dialneter of tenslon reinforcenlent

concrete compressive strength (MPa)

confined concrete 01"1'':'1-. .... 1"1-.

fed design value of concrete strength

;~tl11 concrete lnean tensile strength

ftdd,c design value of FRP (fibre-reinforced polyn1er) effective debonding strength

jfu,w(R)ultin1ate strength of FRP sheet wrapped around corner with radius R, expression (A.25)

.h estimated mean value of steel yield strength

.hd design value of yield strength of (longitudinal) reinforcenlent fyj,d design value of yield strength jacket steel

;;'\"1 yield stress of transverse or confinenlent reinforcelnent h depth of cross-section

kb = ~1,5. (2 - wf /Sf )/(1 + tVf /100 n1n1) reinforced polynler) strips/sheet

coverIng coefficient of FRP (fibre-

n nunlber of spliced bars along perimeter p

p length of perinleter line in column section along the inside of longitudinal

S centreline spacing of stirrups

Sf centreline spacing of FRP (fibre-reinforced polymer) strips for FRP sheets)

tf thickness of FRP (fibre-reinforced polYlner) sheet

tj thickness of steel jacket

x conlpression zone depth

Wf width of FRP (fibre-reinforced polymer) strip/sheet

z length of section internal lever ann

Ae colunln cross-section area

Af trlevrSinp : horizontally projected cross-section area of FRP (fibre-reinforced polymer) strip/sheet with thickness tt~ \vidth Wf and angle p

As cross-sectional area of longitudinal steel reinforcenlent

Asw cross-sectional area of stilTup

Ef FRP (fibre-reinforced polymer) modulus

Ly=M/V shear span at menlber end

N axial force (positive for cOlnpression)

VR,c shear resistance of lnember without web reinforcement

VR,l11ax shear resistance as detennined by crushing in the diagonal compression strut

Vw contribution of transverse reinforcenlent to shear resistance

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a confinen1ent effectiveness factor

rc] factor, greater than 1,0 for prin1ary selSl111C and equal to 1,0 for secondary seismic elen1ents

It'd partial factor for FRP (fibre-reinforced polY111er) debonding

() angle between the diagonal and the axis of a column

Bell concrete ultin1ate strain

Bill FRP (fibre-reinforced polyn1er) ultin1ate strain

Dsu.w ultimate strain of confinen1ent reinforcen1ent

B strut inclination angle in shear design

By chord rotation at yielding of concrete lueluber

Bu ultimate chord rotation of concrete meluber

v = N / bl?f~ (b width of cOlupression zone)

Pd steel ratio of diagonal reinforcement

Pf volun1etric ratio of FRP (fibre-reinforced polyn1er)

ps geometric steel ratio

psx / bwSh = ratio of transverse steel parallel to direction x of loading (sh

stirrup spacing)

Plot total longitudinal reinforcetnent ratio

Psw volun1etric ratio of confinen1ent reinforcen1ent

pw transverse reinforcement ratio

qJu ultin1ate curvature at end section

fA, yield curvature at end section

(0, (0 n1echanical reinforceluent ratio of tension and compression reinforcement

1.6.3 Symbols used in Annex B

bep width of the cover plate

bf flange width

de column depth

dz panel-zone depth between continuity plates

e distance between the plastic hinge and the column face

f~ concrete cOlupressive strength

f~t tensile strength of the concrete

IlIw tensile strength of the welds yield strength of transverse reinforcen1ent

,h,p] n01111nal yield strength of each flange

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lcp length of the cover plate

tep thickness of the cover plate

tf thickness

web thickness

W z panel-zone width between column ~''''',L.''''''''U

A g area of the section

Ahf area of the haunch flange

ApI area of each flange

Bs width of the steel flat-bar brace

B width of the COlTIposite section

E Young's modulus of the beam

elastic nlodulus of the RC (reinforced concrete) panel

F t seisnlic base shear

H frame height

He storey height of the fralne

K{p connection rotation stiffhess

1 lTIOlTIent of inertia

L bealTI span

A1pb,Rd beam plastic nlonlent

Nd design axial

Ny yield strength of the steel brace

Sx beam elastic (n1ajor) modulus;

Tc thickness of the panel

Vpl,Rd,b shear force at a bean1 plastic hinge

Zb plastic modulus of the beanl

BS EN 1998-3:2005 EN 1998-3:2005 (E)

effective plastic lTIodulus of the section at the plastic hinge location

pw ratio of transverse reinforcement

1. 7 S.I. Units

(1) Reference is lTIade to EN 1998-1: 2004, 1.7.

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2 PERFORl\1ANCE REQUIRE~fENTS AND COMPLIANCE CRITERIA

2.1 Fundamental requirements

(1)P The fundmnental requlrelnents refer to the state of danlage in the structure, herein defined through three Linlit States (LS), nalnely Near Collapse (NC), Significant Dall1age (SD), and Dalnage Limitation (DL). These Limit States shall be characterised as follows:

LS of Near Collapse (NC). The structure is heavily dall1aged, with low residual lateral strength and stiffness, although vertical elenlents are still capable of sustaining vertical loads. Most non-structural cOlnponents have col1apsed. Large pern1anent drifts are present. The structure is near collapse and would probably not survive another earthquake, even of moderate intensity.

LS of Significant Danlage (SD). The structure is significantly dan1aged, with son1e residual lateral strength and stiffness, and vertical elenlents are capable of sustaining vertical loads. Non-structural conlponents are dall1aged, although partitions and infills have not failed out-of-plane. Moderate pennanent drifts are present The structure can sustain after-shocks of nloderate intensity. The structure is likely to be unecono111ic to repaIr.

LS of Da111age Linlitation (DL). The structure is only lightly dan1aged, with structural elelnents prevented fron1 significant yielding and retaining their strength and stiffness properties. Non-structural components, such as partitions and infills, l11ay show distributed cracking, but the danlage could be economically repaired. Pennanent drifts are negligible. The structure does not need any repair Ineasures.

NOTE The definition of the Limit State of Collapse given in this Part 3 of Eurocode 8 is closer to the actual col1apse of the building than the one given in EN 1998-1: 2004 and corresponds to the fullest exploitation of the deformation capacity of the structural elements. The Limit State associated with the 'no collapse' requirement in EN 1998-1: 2004 is roughly equivalent to the one that is here defined as Limit State of Significant Damage.

(2)P The National Authorities decide whether all three Lin1it States shall be checked, or two of them, or just one of them.

NOTE The choice of ~ the Limit States to be checked in a country @1] , among the three Limit States defined in 2.1(1)P, may be found in the National Annex.

(3)P The appropriate levels of protection are achieved by selecting, for each of the Limit States, a return period for the seisn1ic action.

14

NOTE The return periods ascribed to the various Limit States to be checked in a country may be found in its National Annex. The protection normally considered appropriate for ordinary new buildings is considered to be achieved by selecting the following values for the return periods:

LS of Near Collapse (NC): 2.475 years, corresponding to a probability of exceedance of2% in 50 years

- LS of Significant Damage (SO): 475 years, corresponding 10 a probability of exceedance of 10% in 50 years LS of Damage Limitation (DL): 225 years, corresponding to a probability of exceedance of 20% in 50 years.

2.2 Compliance criteria

2.2.1 General

BS EN 1998-3:2005 EN 1998-3:2005 (E)

(I)P Compliance with the requirements in 2. t is achieved by adoption of the seisn1ic action, Inethod of analysis, verification and detailing procedures contained in this part of EN 1998, as appropriate for the ditIerent structural materials within its scope (i.e. concrete, steel, 111asonry).

(2)P Except when using the q-factor approach, compliance is checked by making use of the full (unreduced, elastic) SeiSll1ic action as defined in 2.1 and 4.2 for the appropriate return period.

(3)P For the verification of the structural elen1ents a distinction is n1ade between 'ductile' and 'brittle' ones. Except when using the q-factor approach, the forn1er shall be verified by checking that de111ands do not exceed the cOlTesponding capacities in te1111S of defonnations. The latter shall be verified by checking that den1ands do not exceed the corresponding capacities in tern1S of strengths.

NOTE Information for classifying components/mechanisms as "ductile" or "brittle" may be found in the relevant material-related Annexes.

(4)P Alternatively, a q-factor approach lnay be used, where use is made of a seismic action reduced by a q-factor, as indicated in 4.2(3)P. In safety verifications all structural elelnents shall be verified by checking that den1ands due to the reduced seisn11c action do not exceed the corresponding capacities in ter111S of strengths evaluated in accordance with (5) P.

(5)P For the calculation of the capacities of ductile or brittle elements, where these will be con1pared with den1ands for safety verifications in accordance with (3)P and (4)P, n1ean value properties of the existing materials sha11 be used as directly obtained from in-situ tests and fron1 the additional sources of inforn1ation, appropriately divided by the confidence factors defined in 3.5, accounting the level of knowledge attained. Nominal properties shall be used for new or added n1aterials.

(6)P Son1e of the existing structural elen1ents 111ay be designated as "secondary seisn1ic", in accordance with the definitions in EN 1998-1: 2004, 4.2.2 (1 )P, (2) and (3). "Secondary seis111ic" elen1ents shall be verified with the saIne conlpliance criteria as primary seisInic ones, but using less conservative estin1ates of their capacity than for the elelnents considered as "prin1ary seislnic".

(7)P In the calculation of strength capacities of brittle "prinlary seismic"elenlents, n1aterial strengths sha11 be divided by the partial factor of the material.

NOTE: The values ascribed to the partial factors for concrete, structural masonry and other materials for LIse in a country can be found in the National Annex to this standard. Notes to clauses 5.2.4(3), 6.1.3(1), 7.1.3(1) and 9.6(3) in EN1998-J: 2004 refer to the values of partial factors for steel, concrete, structural steel and masonry to be used for the design of new buildings in different countries.

2.2.2 Limit State of Near Collapse (NC)

(l)P Demands shall be based on the design seisnlic action relevant to this Lilnit State. For ductile and brittle elelnents delnands shall be evaluated based 011 the results

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BS EN 1998-3:2005 EN 1998-3:2005 (E)

of the analysis. If a linear method of analysis is used, denlands on brittle elenlents shall be modified in accordance to 4.5.1 (1 )P.

(2)P Capacities shall be based on appropriately defined ultilnate defornlations for ductile elenlents and on ultin1ate strengths for brittle ones.

(3) The q-factor approach (see 2.2.1(4)P, 4.2(3)P) is generally not suitable for checking this Lin1it State.

NOTE The values of q = 1,5 and 2,0 quoted in 4.2(3)P for reinforced concrete and steel structures, respectively, as well as the values of q possibly justified with reference to the local and global available ductility in accordance with the relevant provisions of EN 1998-1: 2004, correspond to fulfilment of the Damage Limit State. If it is chosen 10 use this approach to check the Near Limit State, then 2.2.3(3)P may be with a value of the q-factor exceeding those in 4.2(3)P by about one-third.

2.2.3 Limit State of Significant Damage (SD)

(1 )P Denlands shall be based on the design selsn1ic action relevant to this LinTit State. For ductile and brittle elements denlands shall be evaluated based on the results of the analysis. In case a linear nlethod of analysis is used, detnands on brittle elenlents shal1 be n10dified in accordance to 4.5.1(1)P.

(2)P Except when using the q-factor approach, capacities shall be based on danlage-related defonnations for ductile elelnents and on conservatively estimated strengths for brittle ones.

(3)P In the q-factor approach (see 2.2.1(4)P, 4.2(3)P), delnands shall be based on the reduced seisnlic action and capacities shall be evaluated as for non-seislnic design situations.

2.2.4 Limit State of Damage Limitation (DL)

(l)P Denlands shall be based on the design seismic action relevant to this Limit State.

(2)P Except when using the q-factor approach, capaCItIes shall be based on yield strengths for all structural elements, both ductile and brittle. Capacities of infil1s shall be based on mean interstorey drift capacity for the infills.

(3)P In the q-factor approach (see 2.2.1(4)P, 4.2(3)P), denlands and capacities shall be c0111pared in ternlS of nlean interstorey drift.

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BS EN 1998·3:2005 EN 1998-3:2005 (E)

3 INFORMATION FOR STRUCTURAL ASSESSlVIENT

3.1 General information and history

(l)P In assessing the earthquake resistance of existing structures, the input data shall be col1ected from a variety of sources, including:

- available docun1entation specific to the building in question,

relevant data sources (e.g. contemporary codes and standards),

- field investigations and,

in nl0st cases, in-situ and/or laboratory measuren1ents and tests, as described 111 lTIOre detail in 3.2 and 3.4.

(2) Cross-checks should be made between the data collected from different sources to n1inilnise uncertainties.

3.2 Required input data

(I) In general, the infonnation for structural evaluation should cover the following points fron1 a) to i).

a) Identification of the structural systen1 and of its compliance with the regularity criteria in EN 1998-1: 2004, 4.2.3. The information should be collected either fron1 on site investigation or fronl original design drawings, if ava"ilable. In this latter case, infol111ation on possible structural changes since construction should also be collected.

b) Identification of the type of building foundations.

c) Identification of the ground conditions as categorised in EN 1998-1: 2004, 3.1.

d) I11fonllation about the overall din1ensions and cross-sectional properties of the building elenlents and the lnechanical properties and condition of constituent lnaterials.

e) Infol111atio11 about identifiable nlaterial defects and inadequate detailing.

f) Infornlation on the seismic design criteria used for the initial design, including the value of the force reduction factor (q-factor), if applicable.

g) Description of the present and/or the planned use of the building (with identification of its inlportance class, as described in 1998-1: 2004, 4.2.5).

h) Re-asseSSll1ent of in1posed actions taking into account the use of the building.

i) Infon11ation about the type and extent of previous and present structural dan1age, if any, including earlier repair l11easures.

(2)P Depending on the an10unt and quality of the inf01111ation collected on the points above, different types of analysis and different values of the confidence factors shall be adopted, as indicated in 3.3.

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BS EN 1998-3:2005 EN 1998-3:2005 (E)

3.3 Knowledge levels

3.3.1 Definition of knowledge levels

(1) For the purpose of choosing the adlnissible type of analysis and the appropriate confidence factor values, the fo11owing three knowledge levels are defined:

KL I : Limited knowledge

KL2 : Nornlal knowledge

KL3 : Full knowledge

(2) The factors detennining the appropriate knowledge level (i.e.KL1, KL2 or KL3) are:

i) geomeuy: the geOlnetrical properties of the structural systeln, and of such non-structural elenlents (e.g. nlasonry infill panels) as nlay affect structural response.

ii) details: these include the anlount and detailing of reinforcenlent in reinforced concrete, connections between 111embers, the connection of floor diaphragms to lateral resisting structure, the bond and nl0rtar jointing of nlasonry and the nature of any reinforcing elenlents in Inasonry,

jii) materials: the mechanical properties of the constituent materials.

(3) The knowledge level achieved detennines the allowable nlethod of analysis (see 4.4), as well as the values to be adopted for the confidence factors (CF). The procedures for obtaining the required data are given in 3.4.

(4) The relationship between knowledge levels and applicable Inethods of analysis and confidence factors is illustrated in Table 3.1. The definitions of the terms 'visual', 'full', 'limited', 'extended' and 'cOlnprehensive' in the Table are given in 3.4.

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BS EN 1998-3:2005 EN 1998-3:2005 (E)

Table 3.1: Knowledge levels and corresponding methods of analysis (LF: Lateral Force procedure, lVIRS: Modal Response Spectrum analysis) and confidence

factors (CF) .

. Knowledge GeOlnetry Details ]\Irateri al s Analysis CF

Level

Sinlulated design Default values in

in accordance wlthaccordance with

relevant practice standards of the

KLI and tilne of LF- MRS Icons tructi on fronl limited in-

situ inspection and

fronl limited in-

situ testing

From inconlplete F r0111 original

original detailed design Fronl original construction specifications with

outline construction drawings with .limited in-situ

KL2 drawings with limited il1-5;itll Itesting All

sanlple visual inspection PI' survey

fron1 extended in-or or

from full froln extended in- situ testing survey situ inspection

F rOln original FrOln original test

detailed reports with

construction limited in-situ

drawings with testing

I

KL3 limited in-situ or All CFKL3 inspection fro

or comprehensive

from in-situ testing

comprehensive

in-situ inspection

NOTE The values ascribed to the confidence factors to be used in a country may be found in its National Annex. The recommended values are CF KL1 = 1,35, CFKL2 = 1,20 and CFKL3 1,00.

3.3.2 KLl: Limited kno·wledge

(1) KL 1 corresponds to the following state of knowledge:

i) geo1Jwtly: the overall structural geonletry and melnber are known either (a) from survey; or (b) froln original outline construction drawings used for both the

19

BS EN 1998-3:2005 EN 1998-3:2005 (E)

original construction and any subsequent Inodifications. In case (b), a sufficient san1ple of dimensions of both overall geometry and n1en1ber sizes should be checked on site; if there are significant discrepancies fron1 the outline construction drawings, a fuller din1ensionaJ survey should be perfonned.

ii) details: the structural details are not known frOln detailed construction drawings and n1ay be assumed based on sin1ulated design in accordance with usual practice at the time of construction; in this case, limited inspections in the n10st critical elen1ents should be perfo1111ed to check that the assumptions conespond to the actual situation. Otherwise~ n10re extensive in-situ inspection is required.

iii) materials: no direct inforn1ation on the nlechanical properties of the construction ll1aterials is available, either fronl original design specifications or from Ol-jginal test reports. Default values should be assunled in accordance with standards at the tjnle of construction, accOlTIpanied by limited in-situ testing in the Inost critical elenlents.

(2) The inforn1ation collected should be sufticient for perforn1ing local verifications of element capacity and for setting up a linear structural analysis Inodel.

(3) Structural evaluation based on a state of limited knowledge should be perfornled through linear analysis methods, either static or dynamic (see 4.4).

3.3.3 KL2: Normal knowledge

(I) KL2 corresponds to the following state ofla10wledge:

i) geometr:v: the overall structural geon1etry and member sizes are known either (a) from an extended surveyor (b) from outline construction drawings used for both the original construction and any subsequent lTIodifications. In case (b), a sufficient sample of dinlensions of both overall ge0111etry and melYlber should be checked on site; if there are significant discrepancies from the outline construction drawings, a fuller dimensional survey is required.

ii) details: the structural details are known either frOlTI extended in-situ inspection or frOln inconlplete detailed construction drawings. In the latter case, liInited in-situ inspections in the 1110st critical elements should be perforn1ed to check that the available inforn1ation corresponds to the actual situation.

iii) materials: inforn1ation on the n1echanical properties of the construction Inaterials is available either fron1 extended in-situ testing or fron1 original design specifications. In this latter case, lin1ited in-situ testing should be performed.

(2) The inforn1ation collected should be sufficient for perfornling local verifications of elen1ent capacity and for setting up a linear or nonlinear structural model.

(3) Structural evaluation based on this state of knowledge ll1ay be perforn1ed through either linear or nonlinear analysis methods, either static or dynanlic (see 4.4).

3.3.4KL3: Full knowledge

(1) KL3 corresponds to the following state of knowledge:

i) geometry: the overall structural geon1etry and menlber sizes are known either (a)

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BS EN 1998-3:2005 EN 1998-3:2005 (E)

from a conlprehensive survey or (b) fr01n the c0111plete set of outline construction drawings used for both the original construction and any subsequent nlodifications. [11 case (b), a sufficient saInple of both overall gemnetry and 111enlber sizes should be checked on site; jf there are significant discrepancies fro111 the outline construction drawings, a fuller dinlensional survey is required.

ii) detaiL)': the structural details are known either fr0111 comprehensive in-situ inspection or [f0111 a conlplete set of detailed construction drawings. In the latter case, linlited in-situ inspections in the 1nost critical elenlents should be performed to check that the available infornlation corresponds to the actual situation.

iii) materials: infornlation on the 111echanical properties of the construction nlaterials is available either frol11 comprehensive in-situ testing or fronl original test reports. In this latter case, lilnited in-situ testing should be performed.

(2) 3.3.3(2) applies.

(3) 3.3.3(3) applies.

3.4 Identification of the Knowledge Level

3.4.1 Geometry

3.4.1.1 Outline construction drawings

(1) The outline construction drawings are those docunlents that describe the geoll1etry of the structure, allowing for identification of structural c01nponents and their dimensions, as well as the structural systenl to resist both vertical and lateral actions.

3.4.1.2 Detailed construction dra\vings

(1) The detailed drawings are those docunlents that describe the geometry of the structure, allowing for identification of structural conlponents and their dinlensions, as well as the structural system to resist both vertical and lateral actions. In addition, they contain infomlation about details (as specified in 3.3.1(2)).

3.4.1.3 Visual survey

(1) A visual survey is a procedure for checking correspondence between the actual geometry of the structure with the available outline construction drawings. Sample geOlnetry Ineasurell1ents on selected elelnents should be carried out. Possible structural changes which Inay have occurred during or after construction should be subjected to a survey as in 3.4.1.4.

3.4.1.4 Full survey

(1) A full survey is a procedure resulting in the production of structural drawings that describe the gemnetry of the structure, allowing for identification of structural cOll1ponents and their dilnensions, as well as the structural systeln to resist both vertical and lateral actions.

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BS EN 1998-3:2005 EN 1998-3:2005 (E)

3.4.2 Details

(1) Reliable non-destructive nlethods may be adopted in the inspections specified as follows:

3.4.2.1 Simulated design

(1) A sin1ulated design is a procedure resulting in the definition of the mnount and layout of reinforcenlent, both longitudinal and transverse, in all elements participating in the vertical and lateral resistance of the building. The design should be canied out based on regulatory docLlnlents and state of the practice used at the time of construction.

3.4.2.2 Limited in-situ inspection

(I) A l1111ited in-situ inspection is a procedure for checking correspondence between the actual details of the structure with either the available detailed construction drawings or the results of the sin1ulated design in 3.4.2.1. This entails perfornling inspections as indicated in 3.4.4(1 )P.

3.4.2.3 Extended in-situ inspection

(I) An extended in-situ inspection is a procedure used when the original detailed construction drawings are not available. This entails perfonning inspections as indicated in 3.4.4(1)P.

3.4.2.4 Comprehensive in-situ inspection

(1) A conlprehensive in-situ inspection is a procedure used when the original detailed construction drawings are not available and when a higher knowledge level is pursued. This entails perfonning inspections as indicated in 3.4.4(I)P.

3.4.3 1\1aterials

3.4.3.1 Destructive and non-destructive testing

(I) Use of non-destructive test methods (e.g., Schnlidt halnmer test, etc.) should be considered; however such tests should not be used in isolation, but only in conjunction with destructive tests.

3.4.3.2 Lhnited in-situ testing

(1) A lin1ited progranlnle of in-situ testing is a procedure for conlplenlenting the infofnlation on nlaterial properties derived either froll1 standards at the till1e of construction, or from original design specifications, or from original test reports. This entails perfoffi1ing tests as indicated in 3.4.4(1)P. However, if values fronl tests are lower than default values in accordance with standards of the time of construction, an extended in-situ testing is required.

3.4.3.3 Extended in-situ testing

(I) An extended progrmnn1e of in-situ testing is a procedure for obtaining infonnation when neither the original design specification nor the test reports are

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BS EN 1998-3:2005 EN 1998-3:2005 (E)

available. This entails perfoll11ing tests as indicated in 3.4.4(1)P.

3.4.3.4 Comprehensive in-situ testing

(1) A con1prehensive progran1me of in-situ testing is a procedure for obtaining info1111ation when neither the original design specification nor the test reports are available and when a higher IG10wledge level is pursued. This entails performing tests as indicated in 3.4.4(l)P.

3.4.4 Definition of the levels of inspection and testing

(l)P The classification of the levels of inspection and testing depend on the percentage of structural elen1ents that have to be checked for details, as we]] as on the number of n1aterial san1ples per floor that have to taken for testing.

NOTE The amollnt of inspection and testing to be used in a country may be found in its National Annex. For ordinary situations the recommended minimum values are in Table 3.2. There might be cases requiring modifications to increase some of them. These cases 'will be indicated in the National Annex.

Table 3.2: Recommended minimum requirements for diffel'ent levels of inspection and testing.

Inspection (of details) Testing (of materials) i

For each type of primary element (beam, column, wall): I

Level of inspection and Percentage of elements that are Material samples per floor

!

testing checked for details

Limited 20 1

. Extended 50 2

! Comprehensive 80 3

3.5 Confidence factors

(l)P To detennine the properties of existing Inaterials to be used in the ca1culation of the capacity, when capacity is to be compared with den1and for safety verification, the mean values obtained f1'o111 in-situ tests and fro111 the additional sources of inforIl1ation, shall be divided by the confidence factor, CF, given in Table 3.1 for the appropriate knowledge level (see 2.2.1(5)P).

(2)P To detennine the properties to be used in the calculation of the force capacity (strength) of ductile components delivering action effects to brittle cOlnponents/ ll1echanisms, for use in 4.5.1(1 )P(b), the n1ean value properties of existing 111aterials obtained fron1 in-situ tests and f1'o111 the additional sources of information, shall be multiplied by the confidence factor, CF, given in Table 3.1 for the appropriate knowledge level.

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BS EN 1998-3:2005 EN 1998-3:2005 (E)

4 ASSESSMENT

4.1 General

(1) Assessn1ent is a quantitative procedure for checking whether an eXlstmg undanlaged or dmnaged building will satisfy the required lin1it state appropriate to the seisn1ic actio11 under consideration, as specified in 2.1.

(2)P This Standard is intended for the assessment of individual buildings, to decide on the need for structural intervention and to design the retrofitting 111easures that may be necessary. It is not intended for the vulnerability assessn1ent of populations or groups of buildings for seisnlic risk evaluation for various purposes (e.g. for detern1ining insurance risk, for setting risk mitigation priorities, etc.).

(3)P The assessment procedure shall be carried out by means of the general analysis methods specified in EN 1998-1: 2004, 4.3, as n10dified in this Standard to suit the specific problems encountered in the assessn1ent.

(4) Whenever possible, the Inethod used should incorporate information of the observed behaviour of the san1e type of building or similar buildings during previous earthquakes.

4.2 Seismic action and seismic load combination

(l)P The basic n10dels for the definition of the seisn1ic 1110tion are those presented in EN 1998-1: 2004, 3.2.2 and 3.2.3.

(2)P Reference is n1ade in particular to the elastic response spectrun1 specified in EN 1998-1: 2004, 3.2.2.2, scaled to the values of the design ground acceleration established for the verification of the different Lilnit States. The alten1ative representations allowed in EN 1998-1: 2004, 3.2.3 in tenns of either artificial or recorded accelerogrmns are also applicable.

(3)P In the q-factor approach (see 2.2.1(4)P), the design spectIun1 for linearanalysis is obtained fron1 EN 1998-1: 2004, 3.2.2.5. A value of q = 1,5 and 2,0 for reinforced concrete and steel stluctures, respectively, may be adopted regardless of the stIuctural type. Higher values of q may be adopted if suitably justified with reference to the local and global available ductility, evaluated in accordance with the relevant provisions of EN 1998-1: 2004.

(4)P The design seisnlic action shall be combined with the other appropriate permanent and variable actions in accordance with EN 1998-1: 2004, 3.2.4.

4.3 Structural modelling

(I)P Based on infonnation col1ected as indicated in 3.2, a lnodel of the structure shal I be set up. The Inodel shall be such that the action effects in all structural elen1ents can be detell11ined under the seislnic load cOlnbination given in 4.2.

(2)P All provisions of EN 1998-1: 2004 regarding nl0delling (EN 1998-1: 2004, 4.3.1) and accidental torsional effects (EN 1998-1: 2004, 4.3.2) shall be applied without

24

lTIodifications.

BS EN 1998-3:2005 EN 1998-3:2005 (E)

(3) The strength and the stiftlless of secondary seisll1ic elements, 2.2.1(6)P) against lateral actions nlay in general be neglected in the analysis.

(4) Taking into account secondaIY seisnlic elenlents in the overall structural model, however, is advisable if nonlinear analysis is applied. The choice of the elements to be considered as secondary seisn1ic may be varied after the results of a prelilninary analysis. In no case the selection of these elen1ents should be such as to change the classification of the struchIre fron1 non regular to regular, in accordance with the definitions in EN 1998-1: 2004, 4.2.3.

(5)P Mean values of n1aterial properties shall be used in the structuralluodel.

4.4 Methods of analysis

4.4.1 General

(1) The seist11ic action effects, to be combined with the effects of the other permanent and variable loads in accordance with the seisnlic load conlbination in 4.2( 4)P, may be evaluated using one of the following n1ethods:

lateral force analysis (linear),

- lTIodal response spectru111 analysis (linear),

- 11on-l inear static (pushover) analysis,

- non-linear tilDe history dyna111ic analysis.

- q-factor approach.

(2)P Except in the q-factor approach of 2.2.1(4)P and 4.2(3)P, the seislnic action to be used shall be the one conesponding to the elastic (i.e., un-reduced by the behaviour factor q) response spectrum in EN 1998-1: 2004, 3.2.2.2, or its equivalent alternative representations in EN 1998-l: 2004, 3.2.3.

(3)P In the q-factor approach of2.2.1(4)P the seislnic action is defined in 4.2(3)P.

(4) Clause 4.3.3.1(5) ofEN1998-1: 2004 applies.

(5) The above-listed methods of analysis are applicable subject to the conditions specified in 4.4.2 to 4.4.5, with the exception of n1asonry structures for which procedures accounting for the peculiarities of this construction typology need to be used.

NOTE Complementary information on these procedures may be found in the relevant material-related Informative Annex.

4.4.2 Lateral force analysis

(l)P conditions for this n1ethod to be applicable are given in EN 1998-1: 2004~ 4.3.3.2.1, with the addition of the following:

Denoting by D/Cj the ratio between the demand Di obtained fron1 the analysis

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BS EN 1998-3:2005 EN 1998-3:2005 (E)

under the seisnlic load cOll1bination, and the corresponding capacity Cj for the i-tIl 'ductile' prinlary elenlent of the structure (bending monlent in n10ment fran1es or shear walls, axial force in a bracing~ of a braced fraIne, etc.) and by pmux and pmin the Inaximum and 111inimunl values of pi, respectively, over all 'ductile' prin1ary elelnents of the structure with Pi 1, the ratio Pmrj Pmin does not exceed a n1aximum acceptable value in the range of 2 to 3. Around bean1-colull1n joints the ratio Pi needs to be evaluated only at the sections where plastic hinges are expected to fo1'n1 on the basis of the c0111parison of the SU111 of bean1 flexural capacities to that of colUlllns. 4.3(5)P applies for the calculation of the capacities Ci. For the detel111ination of the bending nl0111ent capacities Cj of vertical elen1ents, the value of the axial force 111ay be taken eq ual to that due to the vertical loads only.

NOTE 1 The value ascribed to this limit of Pm;) x/ Pillill for lise in a country (within the range indicated above) may be found in its National Annex. The recommended value is 2,5.

NOTE 2 As an additional condition, the capacity C of the "brittle" elements or lllechanisl11sshould be larger than the corresponding demand D j , evaluated in accordance with 4.5.1 (I)P, (2) and (3). Nonetheless, enforcing it as a criterion for the applicability of linear analysis is redundant, because, in accordance with 2.2.2(2)P, 2.2.3(2)P and 2.2.4(2)P, this condition will ultimately be fulfilled in all elements of the assessed or retrofitted structure, irrespective of the mehod of

(2)P The method shall be applied as described in EN 1998-1: 2004, 4.3.3.2.2, 4.3.3.2.3 and 4.3.3.2.4, except that the ordinate of the response spectrunl in expression (4.5) shall be that of the elastic spectrunl Se(Td instead of the design spectrunl Sd(T1).

4.4.3 lVlulti-modal response spectrum analysis

(l)P The conditions of applicability for this ll1ethod are given in EN 1998-1: 2004, 4.3.3.3.1, with the addHion of the conditions specified in 4.4.2.

(2)P The method shall be applied as described in EN 1998-1: 2004, 4.3.3.3.2/3, using the elastic response spectrunl Se(TI).

4.4.4 Nonlinear static analysis

4.4.4.1 General

(1)P Nonlinear static (pushover) analysis is a non-linear static analysis under constant gravity loads and 1110110tonically increasing horizontal loads.

(2)P Buildings not conforming with the criteria of EN 1998-1: 2004, 4.3.3.4.2.1 (2), (3) for regularity in plan shall be analysed using a spatial nlodel.

(3)P For buildings confornling with the regularity criteria of EN 1998-1: 2004, 4.2.3.2 the analysis nlay be perforn1ed using two planar nl0dels, one for each n1ai11 horizontal direction of the building.

4.4.4.2 Lateral loads

(1) At least two vertical distributions of lateral loads should be applied:

26

a "uniforn1" pattern, based on lateral forces that are proportional to 111ass regardless of elevation (unifor111 response acceleration)

BS EN 1998~3:2005 EN 1998-3:2005 (E)

a "n10dar' pattern, proportional to lateral forces consistent with the lateral force distribution detern11ned in elastic analysis

(2) Lateral loads should be applied at the location of the masses In the 1110del. Accidental eccentricity should be taken into account.

4.4.4.3 Capacity curve

(1) The relation between base-shear force and the control displacement (the "capacity curve") should be detennined in accordance with 1998-1: 2004, 4.3.3.4.2.3(1), (2).

4.4.4.4 Target displacement

(l)P Target displacelnent is defined as in 1998-] : 2004, 4.3.3.4.2.6(1).

NOTE Target displacement may be determined in accordance with EN 1998-1: 2004, Informative Annex B.

4.4.4.5 Procedure for estimation of torsional and higher mode effects

(1)P The procedure given in EN 1998-1: 2004, 4.3.3.4.2.7(1) to (3) applies for the estimation of torsional effects.

(2) In buildings that do not meet the criteria in EN1998-1: 2004, 4.3.3.2.1 (2)a, the contributions to the response fron1 n10des of vibration higher than fundamental one in each principal direction should be taken into account.

NOTE The requirement in (2) may be satisfied either by performing a non-linear time-history analysis in accordance with 4.4.5, or through versions of the non-linear static analysis procedure that can capture the effects modes on global measures of the response (such as interslorey drifts) to be translated then to estimates of 10caJ deformation demands (such as member rotations). The National Annex may contain reference to complementary, non-contradictory information for sllch procedures.

4.4.5 Non-linear time-history analysis

(1)P The procedure given in EN 1998-1: 2004, 4.3.3.4.3(1) to (3) applies.

4.4.6 q-factor approach

(l)P In the q-factor approach, the method shall be applied as described in EN 1998-1: 2004, 4.3.3.2 or 4.3.3.3, as appropriate.

4.4.7 Combination of the components of the seismic action

(l)P two horizontal c0111ponents of the seismic action shall be c0111bined 111 accordance with EN 1998-1: 2004, 4.3.3.5.1.

(2)P The vertical con1ponent of the seismic action shall be taken into account In the cases specified in EN 1998-1: 2004, 4.3.3.5.2 and, when appropriate, con1bined with the horizontal cOlnponents as indicated in the san1e clause.

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BS EN 1998~3:2005 EN 1998-3:2005 (E)

4.4.8 Additional measures for masonry infilled structures

(1) The provisions of EN 1998-1: 2004, 4.3.6 apply, wherever relevant.

4.4.9 Combination coefficients for variable actions

(l) The provisions of EN 1998-\: 2004, 4.2.4 apply

4.4.10 Inlportance classes and importance factors

(1) The provisions oLEN 1998-1: 2004,4.2.5 apply.

4.5 Safety verifications

4.5.1 Linear methods of analysis (lateral force or nlodal response spectrum analysis)

(l)P "'Brittle" components/mechanisnls shall be verified \vith denlands calculated by lneans of equilibriUln conditions, on the basis of the action effects delivered to the brittle component/nlechanism by the ductile conlponents. In this calculation, each action effect in a ductile cOlnponent delivered to the brittle con1ponent/n1echanism under consideration shall be taken equal to:

(a) the valueD obtained frOIU the analysis, if the capacity C of the ductile con1ponent, evaluated using mean values ofn1aterial properties, satisfies p = DIC ~ 1,

(b) the capacity of the ductile cOluponent, evaluated using nlean values of material properties l1lultiplied by the confidence factors, as defined in 3.5, accounting for the level of knowledge attained, if pD/C > 1, withD and C as defined in (a) above.

(2) In (1)b above the capacities of the beanl sections around concrete bealu-co1umn joints should be cOluputed froin expression (5.8) in 1998-1: 2004 and those of the colunln sections around such joints fron1 expression (5.9), using in the right-hand-side of these expressions the value /Rd = 1 and nlean values of material properties 111ultiplied by the confidence factors, as defined in 3.5.

(3) For the calculation of force dernands on the "brittle" shear luechanis11l of walls through (l)b above, expression (5.26) in EN 1998-1: 2004 nlay be applied with YRd 1 and using asMRd the bending monlent capacity at the base, evaluated using mea11 values of Inaterial properties ITIultiplied by the confidence factors, as defined in 3.5.

(4) In (l)P to (3) above the bending n1011lent capacities Ci of vertical elen1ents Inay be based on the value of the axial force due to the vertical loads only.

(5)P The value of the capacity of both ductile and brittle cOluponents and 11lechanis11ls to be con1pared to deluand in safety verifications, shall be in accordance with 2.2.1 (5)P.

NOTE Information for the evaluation of the capacity of components and mechanisms may be found in the relevant material related Informative Annexes Band C.

28

4.5.2 Nonlinear methods of analysis (static or dynamic)

BS EN 1998-3:2005 EN 1998-3:2005 (E)

(l)P The denlands on both "ductile" and "brittle" conlponents shall be those obtained frOlTI the analysis perfomled in accordance with 4.4.4 or 4.4.5, using 111ean value properties of the materials.

(2)P 4.5.1(5)P applies.

NOTE Information for the evaluation of the capacity of components and mechanisms may be found in the relevant material related Informative Annexes A, Band C.

4.5.3 q-factor approach

(l)P The values of both denland and capacity of ductile and brittle melTlbers shall be in accordance with 2.2.1(4)P, 2.2.3(3)P.

4.6 Summary of criteria for analysis and safety verifications

(l)P Table 4.3 sunlnlarises:

The values of the material properties to be adopted in evaluating both the denland and capacities of the elenlents for all types of analysis.

- The criterja that shall be followed for the safety verificatjon of both ductile and brittle elements for all types of analysis.

29

BS EN 1998-3:2005 EN 1998-3:2005 (E)

Table 4.3: Values of material properties and criteria for analysis and safety verifications.

Linear Model (LM) Nonlinear Model q-factor approach Den1and Capacity Den1and Capacity Delnand Capacity

•

Acceptability of Linear Model (for checking of Pi =- D/Cj values): I§)

Fronl lIn tenTIS of In ternlS of

analysis. Usestrength. defor-

111ean valuesU se nlean Ination. of properties values of Use nlean

Ducti1 in model, properties. values of From e Verifications (if LM properties analysis.

accepted): divided In ternlS of by CF. defonnation. 1@i1 Use mean In tenns of

Fronl values of strength.

analysis. From Type of properties analysis.

Use Inean

elenlent or divided by U: values of

Icp. ll1ean properties lnechanislTI values of (elm) Verifications (if LM properties

divided by CF and by

accepted): in model. partial If Pi In terms factor. fron1 of analysis. strength. In If Pi> 1: In terms of Use mean accordance fronl strength. !values of with the

Brittle equilibriull1!USe Inean properties ~elevant with values of idivided Section of strength of properties ~yCF IEN1998-1: ductile e/nl.ldivided by CF and by 2004. Use nlean and by partial partial values of factor. factor properties lTIultiplied byCF.

30

BS EN 1998-3:2005 EN 1998-3:2005 (E)

5 DECISIONS FOR STRUCTURAL INTERVENTION

5.1 Criteria for a structural intervention

5.1.1 Introduction

(1) On the basis of the conclusions of the asseSSlnent of the structure and/or the nature and extent of the dmnage, decisions should be taken for the intervention.

NOTE As in the of ne\-v structures, optimal decisions are pursued, taking into account social aspects, such as the disruption of use or occupancy during the intervention.

(2) Standard describes the technical aspects of the relevant criteria.

5.1.2 Technical criteria

(l)P The selection of the type, technique, extent and urgency of the intervention shall be based on the structural infon11ation collected during the asseSS111ent of the building.

(2) The following aspects should be taken into account:

a) All identified local gross errors should be appropriately relnedied;

b) In case of highly irregular buildings (both in tern1S of stiffness and overstrength distributions), structural regularity should be improved as much as possible, both In elevation and in plan;

c) The required characteristics of regularity and resistance can be achieved by ei ther 1110dification of the strength and/or stiffness of an appropriate l1u111ber of existing components, or by the introduction of new structuralelements;

d) Increase in the local ductility supply should be effected where required;

e) The increase in strength after the intervention should not reduce the available global ductility;

f) Speciflcally for nlasonry structures: non-ductile lintels should be replaced, inadequate connections between floor and wal1s should be ilnproved, out-of-plane horizontal thnlsts against walls should be eliminated.

5.1.3 Type of intervention

(1) An intervention may be selected from the following indicative types:

a) Local or overall tnodification of danlaged or undamaged elen1ents (repair, strengthening or full replacelnent), considering the stiffness, and/or ductility of these elements;

b) Addition of new structural elen1ents bracings or inft]] walls; steel, titl1ber or reinforced concrete belts in Inasonry construction; etc);

c) Modification of the structural systenl (eliInination of SOlne structural joints;

31

BS EN 1998-3:2005 EN 1998-3:2005 (E)

widening of joints; elinlination of vulnerable elenlents; nlodification into 1110re regular and/or nlore ductile arrangenlents) I;

d) Addition of a new structural systenl to sustain some or all of the entire seismic action;

e) Possible transfornlation of existing non-structural elenlents into structural elements;

f) Introduction of passive protection devices through either dissipative bracing or base isolation;

g) Mass reduction;

h) Restriction or change of use of the building;

i) Partial demolition;

(2) One or Inore types in cOlnbination may be selected. In all cases, the effect of structural nlodifications on the foundation should be taken into account.

(3)P If base isolation is adopted, the provisions contained in EN 1998-1: 2004, 10 sha11 be followed.

5.1.4 Non-structural elements

1 (P) Decisions regarding repair or strengthening of non-st1llctural elements shall also be taken whenever, in addition to functional requirenlents, the SeiS111ic behaviour of these elenlents may endanger the life of inhabitants or affect the value of goods stored in the building.

(2) In such cases, full or partial collapse of these elements should be avoided by nleans of:

a) Appropriate connections to structural elements (see EN 1998-1: 2004, 4.3.5);

b) Increasing the resistance of non-structural elelnents (see EN 1998-1: 2004, 4.3.5);

c) Taking measures of anchorage to prevent possible falling out of parts of these elelnents.

(3) The possible consequences of these provisions on the behaviour of structural elenlents should be taken into account.

5.1.5 Justification of the selected intervention type

(l)P In al1 cases, the documents relating to retrofit design shall include the justification of the type of intervention selected and the description of its expected effect on the structural response.

I This is for instance the case when vulnerable low shear-ratio columns or entire soft arc transformed into more ductile arrangements; similarly, when overstrength irregularities in elevation, or in-plan """

(2) This justification should be made available to the owner.

BS EN 1998-3:2005 EN 1998-3:2005 (E)

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BS EN 1998-3:2005 EN 1998-3:2005 (E)

6 DESIGN OF STRUCTURAL INTERVENTION

6.1 Retrotit design procedure

(I)P The retrofit design procedure shall include the following steps:

a) Conceptual design,

b) Analysis,

c) Verifications.

(2)P The conceptual design shall cover the following:

(i) Selection of techniques and/or materials, as well as of the type and configuration of the intervention.

(ii) Prelinlinary estinlation of dilTIensions of additional structural parts.

(iii) PrehlTIinary estilTIation of the lTIodified stiffness of the retrofitted elenlents.

(3)P The methods of analysis of the structure specified in 4.4 shall be used, taking into account the modified characteristics of the building.

(4)P Safety verifications shall be can-ied out in general in accordance with 4.5, for both existing, modified and new structural elements. For existing materials, nlean values from in-situ tests and any additional sources of information shall be used in the safety verification, nlodified by the confidence factor CF, as specified in 3.5. However, for new or added nlaterials nonlinal properties shaH be used, without modification by the confidence factor CF.

NOTE Information on the capacities of and new structural elements may be fOLlnd in the relevant material-related Informative Annex A, B or C.

(5)P In case the structural systeITI, comprising both eXIstIng and new stIuctural elenlents, can be made to fulfill the requirements of EN 1998-1: 2004, the verifications may be canied out in accordance with the provisions therein.

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BS EN 1998-3:2005 EN 1998-3:2005 (E)

ANNEX A (Informative)

REINFORCED CONCRETE STRUCTURES

A.l Scope

(1) This Annex contains specific information for the assessment of reinforced concrete buildings in their present state, and for their upgrading, when necessary.

A.2 Identification of geometry, details and materials

A.2.1 General

(1) The fol1owing aspects should be carefully exanlined:

i. Physical condition of reinforced concrete elements and presence of any degradation, due to carbonation, steel corrosion, etc.

ii. Continuity of load paths between lateral resisting elelTIents.

A.2.2 Geometry

(1) The collected data should include the following itenls:

1. Identification of the lateral resisting systelTIS in both directions.

11. Orientation of one-way floor slabs.

111. Depth and width of beaITIS, COlUITInS and walls.

IV. Width of flanges in T -bealTIs.

V. Possible eccentricities between beams and colull1ns axes at joints.

A.2.3 Details

(1) The collected data should include the following iteiTIs:

1. Amount of longitudinal steel in beanls, colunlns and walls.

11. Anlount and detailing of confining steel in critical regions and in beanl-column joints.

111. AInount of steel reinforcement in floor slabs contributing to the negative resisting bending lTI01nent of T -bemus.

IV. Seating lengths and support conditions of horizontal elenlents.

35

BS EN 1998-3:2005 EN 1998-3:2005 (E)

v. Depth of concrete cover.

VI. Lap-splices for longltudinal reinforcel11ent.

A.2.4 Materials

(l) The collected data should include the following iten1s:

1. Concrete strength.

Steel yield strength, ultilnate strength and ultimate strain.

A.3 Capacity models for assessment

A.3. t Introduction

(I) The provisions given in this clause apply to both prin1ary and secondary seismic elenlents.

(2) Classification of con1ponents/n1echanislTIs:

1. "ductile": beaITI, colun1ns and walls under flexure with and without axial force,

11. "brittle": shear n1echanism of beams, colun1ns, walls and joints.

A.3.2 Beam, columns and walls under flexure with and without axial force

A.3.2.1 Introduction

(l) The deforInation capacity of bea111s, colU111ns and walls, to be verified in accordance with 2.2.2(2)P, 2.2.3(2)P, 2.2.4(2)P, is defined in tefnlS of the chord rotation (), i. e., of the angle between the tangent to the axis at the yielding end and the chord connecting that end with the end of the shear span (Lv M/V = n10n1ent/shear at the end section), , the point of contraflexure. The chord rotation is also equal to the element drift ratio, i. e., the deflection at the end of the shear span with respect to the tangent to the axis at the yielding end, divided by the shear span.

A.3.2.2 Limit State of near collapse (NC)

(l) The value of the total chord rotation capacity (elastic plus inelastic part) at ultinlate, eu , of concrete melnbers under cyclic loading may be calculated fr0111 the following expression:

=_1 0,016. (0,3 f,)[max(o,o 1; oj) ,rclO.225 r mil 9; Lv J' JO.35 2jap" II:" 1 (l,2 SllfO Po ) reI 111ax(O,O 1; OJ) \ 1\ h (A,1) @il where:

rei is equal to 1,5 for prin1ary seislnic elenlents and to 1,0 for secondary seis111ic

36

BS EN 1998-3:2005 EN 1998-3:2005 (E)

elements (as defined in 2.2.1(6)P),

h is the depth of cross-section,

Lv = IV/IV is the ratio 1110n1ent/shear at the end section,

v N / b11f~ (b width of cOlupression zone, N axial force positlve for compression),

(j), (0' is the luechanical reinforcen1ent ratio of the tension (including the web reinforce111ent) and conlpression, respectively, longitudinal reinforcen1ent,

f~ and.hw are the concrete cOlnpressive strength (MPa) and the stirrup yield strength (MPa), respectively, directly obtained as Inean values fron1 in-situ tests, and froln the additional sources of 1nfo1'111ation, appropriately divided by the confidence factors, as defined in 3.5(1)P and Table 3.1, accounting for the level of knowledge attained,

psx ratio of transverse steel parallel to the direction x of loading (,')'/7

stirrup spacing),

Pd is the steel ratio of diagonal reinforcement (if any), in each diagonal direction,

a is the confinelnent effectiveness factor, that n1ay be taken equal to:

(A.2)

where:

bo and is the dimension of confined core to the centreline of the hoop,

bi is the centerline spacing of longitudinal bars (indexed by i) laterally restrained by a stinup conler or a cross-tie along the perin1eter of the cross-section.

In walls the value given by expression (A.1) is luultiplied by 0,58. @l]

If cold-worked brittle is used the total chord rotation capacity above is divided by 1,6.

(2) The value of the plas6c part of the chord rotation capacity of concrete n1en1bers under cyclic loading n1ay be calculated fronl the following expression:

IEJ) f)pl f) - f) =_1 0,0145. (0 25V)[maX(O,o~aJ)J°,3 LIm urn V ' , (0 ° 1 ;'\ - Yel max , ~ OJ)

(A.3) @l]

where the chord rotation at yielding, By, should be calculated in accordance with A.3.2.4, reI is equal to 1,8 for primary seisluic elements and to 1,0 for secondary seismic ones and all other variables are defined as for expression (A.1), .

In walls the value given by expression (A.3) is ll1ultiplied by 0,6.

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BS EN 1998-3:2005 EN 1998-3:2005 (E)

If cold-worked brittle steel is used, the plastic part of the chord rotation capacity is divided by 2.

(3) In n1embers without detailing for earthquake resistance the values given by expressions ~ (A.l) and (A.3) are divided by 1.2 @j] .

(4) (1) and (2) apply to 111enlbers with defornled (high bond) longitudinal bars without lapping in the vicinity of the end region where yielding is expected. If deformed longitudinal bars have straight ends lapped starting at the end section of the Inen1ber - as is often the case in colunlns and walls with lap-splicing starting at floor level - expressions (A. 1 ) and (A.3) should be applied with the value of the conlpression reinforcenlent ratio, 0/ doubled over the value applyjng outside the lap splice. Moreover, if the lap length 10 is less than the plastic part of the chord rotation capacity given in (2) should be n1ultiplied by Ijlou.min, while the value of the chord rotation at yielding, added to it to obtain the total chord rotation capacity, should account for the effect of the lapping in accordance with A.3.2.4(3). The value of lou,min is

1,05+ 14,5 a'Psxlvw(fc)~fcJ,

where:

dbL is the dian1eter of the lapped bars

is the mean value of the yield strength of the lapped bars (NIPa) fr0111 in-situ tests and fron1 the additional sources of info1'n1atlon, n1ultiplied by the corresponding confidence factor, as defined in 3.5 and Table 3.1, accounting for the level of knowledge attained (see 3.5(2)P).

f~,f~\v and psx as defined in (1), and

nrcstr: number of lapped longitudinal bars laterally restrained by a stirrup corner or a cross-tie, and

11'01 : total l1unlber of lapped longitudinal bars along the cross-section perinleter.

(5) In 111enlbers with SI1100th (plain) longitudinal bars without lapping in the vicinity of the end region where yielding is expected, the total chord rotation capacity may be taken equal to the value calculated in accordance with (1) ~ 1111lltiplied by 0,8, while the plastic part of the chord rotation capacity 111ay be taken to be equal to that calculated in accordance with (2) multiplied by 0,75 (with these factors including the reduction factor l,2 of (3) accounting for the lack @j] of detailing for earthquake resistance). If the longitudinal bars are lapped starting at the end section of the n1en1ber and their ends are provided with standard hooks and a lap length 10 of at least 15dbL, the chord rotation capacity of the n1en1ber may be ca1culated as follows:

In expressions (A.!), (A.3) the shear span (ratio Jv!IV - tnoment/shear - at end section) is reduced by the lap length 10' as the ulti111ate condition is controlled by the region right after the end of the lap.

- The total chord rotation capacity nlay be taken equal to the value calculated in ~ accordance with (1) and (3) l11ultiplied by 0,019 (1 ° + n1in( 40, Ijdbd), while the @j] 38

BS EN 1998-3:2005 EN 1998-3:2005 (E)

plastic part of the chord rotation capacity Inay be taken equal to that calculated in ~ accordance with (2) and (3) multiplied by 0,019 mine 40, lo/dbd.

(6) For the evaluation of the ultinlate chord rotation capacity an alternative expression tnay be used:

Bum = 1

(AA) reI

\vhere

By is the chord rotation at yield as defined by expressions (A. 1 0) or (A. I I ),

¢u is the ultitnate curvature at the end section,

rA is the yield curvature at the end section.

The value of the length of the plastic hinge depends on how the enhancenlent of strength and deformation capacity of concrete due to confinelnent is taken into account in the calculation of the ultimate curvature of the end sectlon, rPu.

(7) If the ultimate curvature of the end section ¢u, under cyclic loading is calculated with:

(a) the ultimate strain of the longitudinal reinforcenlent, GSlh taken equal to:

- the nlininlU111 values given in EN 1992-1-1, Table C.I for the characteristic strain at nlaximUln force, Guk, for steel Classes A or B,

- 60/0 for steel Class C, and

(b) the confinenlent nlodeJ in EN 1992-1-1: 2004, 3.1.9, with effective lateral contlning stress 0"2 taken equal to apsx/~w, wbere psx,j~w and a have been defined in (1),

then, for nlembers with deta